21CSS201T

COMPUTER ORGANIZATION
AND ARCHITECTURE

UNIT-1

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Computer Architecture
Objectives
Know the difference between computer organization and computer
architecture.
Understand units of measure common to computer systems
Appreciate the evolution of computers.
Understand the computer as a layered system.
Be able to explain the von Neumann architecture and the function of basic
computer components.

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 COMPUTER ARCHITECTURE AND ORGANIZATION OVERVIEW

• A modern computer is an electronic, digital, general purpose computing machine

that automatically follows a step-by-step list of instructions to solve a problem. This
step-by step list of instructions that a computer follows is also called an algorithm or
a computer program.
• Why to study computer organization and architecture?
• Design better programs, including system software such as compilers, operating
systems, and device drivers.
• Optimize program behavior.
• Evaluate (benchmark) computer system performance.
• Understand time, space, and price tradeoffs.
• Computer organization
• Encompasses all physical aspects of computer systems.
• E.g., circuit design, control signals, memory types.
• How does a computer work?
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 COMPUTER ARCHITECTURE AND ORGANIZATION
OVERVIEW
Focuses on the structure(the way in which the components are interrelated) and
behavior of the computer system and refers to the logical aspects of system
implementation as seen by the programmer
Computer architecture includes many elements such as
instruction sets and formats, operation codes, data types, the number and types
of registers, addressing modes, main memory access methods, and various I/O
mechanisms.
The architecture of a system directly affects the logical execution of programs.
The computer architecture for a given machine is the combination of its hardware
components plus its instruction set architecture (ISA).
The ISA is the interface between all the software that runs on the machine and
the hard
Studying computer architecture helps us to answer the question: How do I
design a computer?

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 COMPUTER ARCHITECTURE AND ORGANIZATION
OVERVIEW

In the case of the IBM, SUN and Intel ISAs, it is possible to purchase processors
which execute the same instructions from more than one manufacturer
All these processors may have quite different internal organizations but they all
appear identical to a programmer, because their instruction sets are the same
Organization & Architecture enables a family of computer models
▪ Same Architecture, but with differences in Organization
▪ Different price and performance characteristics
When technology changes, only organization changes.
This gives code compatibility (backwards)

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 COMPUTER COMPONENTS

At the most basic level, a computer is a device consisting of 3 pieces

A processor to interpret and execute programs
A memory ( Includes Cache, RAM, ROM) to store both data and
program instructions
A mechanism for transferring data to and from the outside world.
I/O to communicate between computer and the world
Bus to move info from one computer component to another
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 Contd..
• Computers with large main memory capacity can run larger programs with
greater speed than computers having small memories.
• RAM is an acronym for random access memory. Random access means that
memory contents can be accessed directly if you know its location.
• Cache is a type of temporary memory that can be accessed faster than RAM.

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 Digital System
• Takes a set of discrete information inputs and discrete internal information
(system state) and generates a set of discrete information outputs.

Discrete Discrete
Inputs Information
Discrete
Processing
Outputs
System

System State
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Signal
• An information variable represented by physical quantity.
• For digital systems, the variable takes on discrete values.
• Two level, or binary values are the most prevalent values in digital systems.
• Binary values are represented abstractly by:
• digits 0 and 1
• words (symbols) False (F) and True (T)
• words (symbols) Low (L) and High (H)
• and words On and Off.
• Binary values are represented by values or ranges of values of physical
quantities

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Introduction to Number System
and Logic Gates

Number Systems- Binary, Decimal, Octal, Hexadecimal

Codes- Grey, BCD,Excess-3,
ASCII, Parity
Binary Arithmetic- Addition, Subtraction, Multiplication, Division using
Sign Magnitude
1’s complement, 2’s complement,
BCD Arithmetic;
Logic Gates-AND, OR, NOT, NAND,
NOR, EX-OR, EX-NOR
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BINARY ARITHMETIC

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 Signed Binary Numbers
• Two ways of representing signed numbers:

• 1) Sign-magnitude form, 2) Complement form.

• Most of computers use complement form for negative number notation.

• 1’s complement and 2’s complement are two different methods in this

type.

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1’s Complement
• 1’s complement of a binary number is obtained by
subtracting each digit of that binary number from 1.
• Example

Shortcut: Invert the numbers from 0 to 1

and 1 to 0

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2’s Complement
• 2’s complement of a binary number is obtained by
adding 1 to its 1’s complement.
• Example

Shortcut: Starting from right side, all bits are same till first 1 occurs and then invert rest
of the bits

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Subtraction using 1’s complement

• Using 1’s complement

• Obtain 1’s complement of subtrahend

• Add the result to minuend and call it intermediate result

• If carry is generated then answer is positive and add the carry to Least
Significant Digit (LSD)

• If there is no carry then answer is negative and take 1’s complement of

intermediate result and place negative sign to the result.

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Subtraction using 2’s complement
• Using 2’s complement
• Obtain 2’s complement of subtrahend

• Add the result to minuend

• If carry is generated then answer is positive, ignore carry and result itself is
answer

• If there is no carry then answer is negative and take 2’s complement of

intermediate result and place negative sign to the result.

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Subtraction using 1’s complement
(Examples)
Example - 1

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Subtraction using 1’s complement
(Examples)
Example - 2

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Subtraction using 2’s complement
(Examples)
Example - 1

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Subtraction using 2’s complement
(Examples)
Example - 2

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BCD ARITHMETIC

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BCD Addition
Example - 1

Rule: If there is an illegal code or carry is generated as a result

of addition, then add 0110 to particular that 4 bits of
result.
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BCD Addition
Example - 2

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BCD Subtraction
Example - 1

Rule: If one 4-bit group needs to take borrow from neighbor, then
subtract 0110 from the group which is receiving borrow.

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BCD Subtraction
Example - 2

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 GRAY CODE
• Gray code is the arrangement of binary number system such that each
incremental value can only differ by one bit.
• This code is also known as Reflected Binary Code (RBC), Cyclic
Code and Reflected Binary (RB). The reason for calling this code as
reflected binary code is the first N/2 values compared with those of the last
N/2 values in reverse order.
• In gray code when transverse from one step to another step the only one bit
will be change of the group. This means that the two adjacent code numbers
differ from each other by only one bit.
• It is popular for unit distance code but it is not use from arithmetic
operations. This code has some application like convert analog to digital,
error correction in digital communication.

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Binary- Gray code conversion

• STEPS
• The most significant bit of gray code is equal to the first bit of the given
binary bit.
• The second bit of gray code will be exclusive-or (XOR) of the first and
second bit of the given binary bit.
• The third bit of gray code is equal to the exclusive-or (XOR) of the second
and third binary bits. For father gray code result this process will be
continuing.

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 Explanation
• The given binary digit is 01001
Truth Table of
XOR
A B C
0 0 0
0 1 1
1 0 1
1 1 0

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Example
• The gray code of the given binary code is (010.01)2 ??
• The first MSB bit of binary is same in the first bit of gray code. In this example the binary
bit is “0”. So, gray bit also “0”.
• Next gray bit is equal to the XOR of the first and the second binary bit. The first bit is 0,
and the second bit is 1. The bits are different so resultant gray bit will be “1” (second
gray codes bit)
• The XOR of the second and third binary bit. The second bit is 1 and third is 0. These bits
are again different so the resultant gray bit will be 1 (third gray codes bit)
• Next we perform the XOR operation on third and fourth binary bit. The third bit is 0,
and the fourth bit is 0. The both bits are same than resultant gray codes will be 0 (fourth
gray codes bit).
• Take the XOR of the fourth and fifth binary bit. The fourth bit is 0 and fifth bit is 1. These
bits are different than resultant gray codes will be 1 (fifth gray code bit)
• The result of binary to gray codes conversion is 01101.

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• You can convert n bit (bnb(n-1)…b2b1b0) binary number to gray code
(gng(n-1)…g2g1g0). For most significant bit bn=gn, and rest of the bit by
XORing b(n-1)=g(n-1)⊕gn, ….

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:

GRAY CODE TABLE

The conversion in between decimal to gray and binary to gray code is
given below
Decimal Binary Number Gray Code
Number
0 0000 0000
The gray code of the given binary code
1 0001 0001
2 0010 0011
(01001) =0 1 1 0 1. We can see one bit change
3 0011 0010
in the next incremental value.
4 0100 0110
5 0101 0111
6 0110 0101
7 0111 0100
8 1000 1100
9 1001 1101
10 1010 1111
11 1011 1110
12 1100 1010
13 1101 1011
14 1110 1001
15 1111 1000

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Gray-Binary code conversion
• STEPS
1. The most significant bit of gray codes is equal in binary number.
2. Now move to the next gray bit, as it is 1 the previous bit will be alter i.e it will be 1, thus
the second binary bit will be 1.
3. Next see the third bit, in this example the third bit is 1 again, the third binary bit will be
alter of second binary bit and the third binary bit will be 0.
4. Now fourth bit of the, here the fourth bit of gray code is 0. So the fourth bit will be same
as a previous binary bit, i.e 4th binary bit will be 0.
5. The last fifth bit of gray codes is 1; the fifth binary number is altering of fourth binary
number.
6. Therefore the gray code (01101) equivalent in binary number is (01001)

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Explanation
Truth Table of
• The given gray code is 01101 XOR
0 1 1 0 1 (Gray) A B C
0 0 0
0 1 1

MSB LSB 1 0 1
1 1 0
Binary code Conversion

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Merits & Demerits of Gray Code
Advantages of gray code
❖ It is best for error minimization in conversion of analog to digital signals.

❖ It is best for minimize a logic circuit

❖ Decreases the “Hamming Walls” which is undesirable state, when used

in genetic algorithms
❖ It is useful in clock domain crossing

Disadvantages of gray code

• Not suitable for arithmetic operations

• It has limited use.

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Binary Codes for Decimal Digits
▪ There are over 8,000 ways that you can chose 10 elements from the 16
binary numbers of 4 bits. A few are useful:

Decimal 8,4,2,1 Excess3 8,4,-2,-1 Gray

0 0000 0011 0000 0000
1 0001 0100 0111 0100
2 0010 0101 0110 0101
3 0011 0110 0101 0111
4 0100 0111 0100 0110
5 0101 1000 1011 0010
6 0110 1001 1010 0011
7 0111 1010 1001 0001
8 1000 1011 1000 1001
9 1001 1100 1111 1000

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Binary Coded Decimal (BCD)
• The BCD code is the 8,4,2,1 code.

• This code is the simplest, most intuitive binary code for decimal
digits and uses the same powers of 2 as a binary number, but only
encodes the first ten values from 0 to 9.

• Example: 1001 (9) = 1000 (8) + 0001 (1)

• How many “invalid” code words are there?

• What are the “invalid” code words?

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 Excess 3 Code and 8, 4, –2, –1 Code
Decimal Excess 3 8, 4, –2, –1
0 0011 0000
1 0100 0111
2 0101 0110
3 0110 0101
4 0111 0100
5 1000 1011
6 1001 1010
7 1010 1001
8 1011 1000
9 1100 1111

• What interesting property is common to these two codes? 61

 Decimal to BCD
•

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Binary to BCD conversion
•

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Advantages of BCD
• Easy to encode and Decode decimals into BCD and Vice-versa
• Easy to implement a hardware algorithm for BCD converter
• Very useful in digital systems whenever decimal information reqd.
– Digital voltmeters, frequency converters and digital clocks all use BCD as
they display output information in decimal.

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Disadvantages of BCD Code
• Require more bits than straight binary code
• Difficult to be used in high speed digital computer when the size and capacity
of their internal registers are restricted or limited.
• The arithmetic operations using BCD code require a complex design of
Arithmetic and Logic Unit (ALU) than the straight binary number system.
• The speed of the arithmetic operations that can be realized using BCD code is
naturally slow due to the complex hardware circuitry involved.
•

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 Excess-3 code
• The excess-3 code is also treated as XS3 code. The
excess-3 code is a non-weighted and self-complementary
BCD code used to represent the decimal numbers.
• This code has a biased representation. This code plays an
important role in arithmetic operations because it resolves
deficiencies encountered when we use the 8421 BCD code
for adding two decimal digits whose sum is greater than 9.
• The Excess-3 code uses a special type of algorithm, which
differs from the binary positional number system or normal
non-biased BCD.

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Decimal to Excess-3 code conversion
Step-1 We find the decimal number of the given binary number.
Step-2 Then we add 3 in each digit of the decimal number.
Step-3 Now, we find the binary code of each digit of the newly
generated decimal number.
Alternatively,
• We can also add 0011 in each 4-bit BCD code of the decimal
number for getting excess-3 code.

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Ex-1
•

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Ex-2
•

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Ex-3
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Excess-3 code

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Ex-4
•

Decimal BCD BCD+ 0011 Excess-3

8 1000 1000+0011 1011

1 0001 0001+0011 0100
6 0110 0110+0011 1001
1 0001
0001+0011 0100

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Ex 5
• Convert 111102 to Excess-3 using binary
• Step 1 Convert binary to Decimal. 111102 = 3010
• Step 2 Add ‘3ʼ to individual digits to decimal number
3 0
3 3
6 3
Step 3: Find binary values of (63)10 = 01100011Excess-3

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Ex 6
• Convert 01100011 Excess-3 to binary.
• Step- 1  Find the decimal by dividing it four digits
• 01100011 Excess-3 = 0110 0011 Excess-3 = 30 10
•Step-2  Find the binary value of the decimal
through division method.
01100011 Excess-3 = 111102

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Advantages
1. These codes are self-complementary.
2. These codes use biased representation.
3. The excess-3 code has no limitation, so that it considerably
simplifies arithmetic operations.
4. The codes 0000 and 1111 can cause a fault in the transmission line.
The excess-3 code doesn't use these codes and gives an
advantage for memory organization.
5. These codes are usually unweighted binary decimal codes.
6. This code has a vital role in arithmetic operations. It is because it
resolves deficiencies which are encountered when we use the 8421
BCD code for adding two decimal digits whose sum is greater than
9.

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 ASCII
•The ASCII stands for American Standard Code for
Information Interchange. The ASCII code is an
alphanumeric code used for data communication in
digital computers.
•The ASCII is a 7-bit code capable of representing 27 or
128 number of different characters. The ASCII code is
made up of a three-bit group, which is followed by a
four-bit code.

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ASCII Characters
• Control Characters-0 to 31 and 127
• Special Characters- 32 to 47, 58 to 64, 91 to 96, and 123 to
126
• Numbers Characters- 0 to 9
• Letters Characters - 65 to 90 and 97 to 122

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Ex 1
• Encode
(10010101100001111011011000011010100111000011011111
101001 110111011101001000000011000101100100110011)2 to
ASCII.

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• Step 1:
• The given binary data is grouped into 7-bits because the ASCII
code is 7 bit.
• 1001010 1100001 1110110 1100001 1010100 1110000 1101111
1101001 1101110 1110100 1000000 0110001 0110010 0110011
• Step 2:
• Then, we find the equivalent decimal number of the binary
digits either from the ASCII table or 64 32 16 8 4 2 1 scheme.

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Cont’d
Binary 64 32 16 8 4 2 1 DECIMAL ASCII
1100011 1 1 0 0 0 1 1 99 C
1101111 1 1 0 1 1 1 1 111 O
1101101 1 1 0 1 1 0 1 109 M
1110000 1 1 1 0 0 0 0 112 P
1110101 1 1 1 0 1 0 1 117 U
1110100 1 1 1 0 1 0 0 116 T
1100101 1 1 0 0 1 0 1 101 E
1110010 1 1 1 0 0 1 0 114 R

So the given binary digits results in ASCII Keyword COMPUTER

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Parity Code
• The parity code is used for the purpose of detecting errors during the
transmission of binary information. The parity code is a bit that is
included with the binary data to be transmitted.
• The inclusion of a parity bit will make the number of 1’s either odd or
even. Based on the number of 1’s in the transmitted data, the parity
code is of two types.
• Even parity code
• Odd parity code

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• In even parity, the added parity bit will make the total number of 1’s
an even number.
• If the added parity bit make the total number of 1’s as odd number,
such parity code is said to be odd parity code.

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Explanation

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• On the receiver side, if the received data is other than the sent data, then it
is an error. If the sent date is even parity code and the received data is odd
parity, then there is an error.

• So, both even and odd parity codes are used only for the detection of error
and not for the correction in the transmitted data. Even parity is commonly
used and it has almost become a convention.

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 Logic Gates
Goal:
To understand how digital a computer can work, at the
lowest level.

To understand what is possible and the limitations of what

is possible for a digital computer.

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 Logic Gates
• All digital computers for the past 50 years have been
constructed using the same type of components.
• These components are called logic gates.
• Logic gates have been implemented in many different
ways.
• Currently, logic gates are most commonly implemented
using electronic VLSI transistor logic.

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 Logic Gates
• A logic gate is a simple switching circuit that determines whether an input pulse can pass through
to the output in digital circuits.

• The building blocks of a digital circuit are logic gates, which execute numerous logical operations
that are required by any digital circuit.

• These can take two or more inputs but only produce one output.

• The mix of inputs applied across a logic gate determines its output. Logic gates use Boolean
algebra to execute logical processes.

• Logic gates are found in nearly every digital gadget we use on a regular basis.

• Logic gates are used in the architecture of our telephones, laptops, tablets, and memory devices.

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 Logic Gates
All basic logic gates have the ability to accept either one or two input
signals (depending upon the type of gate) and generate one output
signal.

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 Truth Table
• The outputs for all conceivable combinations of inputs that may be applied to a logic gate or circuit are

listed in a truth table.

• When we enter values into a truth table, we usually express them as 1 or 0, with 1 denoting True logic

and 0 denoting False logic.

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Classification

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Basic Logic Gates-

• Basic Logic Gates are the fundamental logic gates using which
universal logic gates and other logic gates are constructed.

They have the following properties-

• Basic logic gates are associative in nature.
• Basic logic gates are commutative in nature.

There are following three basic logic gates-

1. AND Gate
2. OR Gate
3. NOT Gate

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AND gate
• The output of AND gate is high (‘1’) if all of its inputs are high (‘1’).
• The output of AND gate is low (‘0’) if any one of its inputs is low
(‘0’).

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 OR Gate
The output of OR gate is high (‘1’) if any one of its inputs is high (‘1’).
The output of OR gate is low (‘0’) if all of its inputs are low (‘0’).
Logic Symbol-

The logic symbol for OR Gate is as shown below-

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 NOT Gate
• The output of NOT gate is high (‘1’) if its input is low (‘0’).
• The output of NOT gate is low (‘0’) if its input is high (‘1’).
From here-
• It is clear that NOT gate simply inverts the given input.
• Since NOT gate simply inverts the given input, therefore it is
also known as Inverter Gate.

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 Universal Logic Gates
Universal logic gates are the logic gates that are capable of implementing
any Boolean function without requiring any other type of gate.
They are called as “Universal Gates” because-
• They can realize all the binary operations.
• All the basic logic gates can be derived from them.

They have the following properties-

• Universal gates are not associative in nature.
• Universal gates are commutative in nature.

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 NAND GATE
• A NAND Gate is constructed by connecting a NOT Gate at the output
terminal of the AND Gate.
• The output of NAND gate is high (‘1’) if at least one of its inputs is low
(‘0’).
• The output of NAND gate is low (‘0’) if all of its inputs are high (‘1’).

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 NOR Gate
• A NOR Gate is constructed by connecting a NOT Gate at the
output terminal of the OR Gate.
• The output of OR gate is high (‘1’) if all of its inputs are low (‘0’).
• The output of OR gate is low (‘0’) if any of its inputs is high (‘1’).

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 EX-OR
• An XOR gate (also known as an EOR, or EXOR gate) – pronounced as “Exclusive OR
gate” – is a digital logic gate that gives a true (i.e. a HIGH or 1) output when the
number of true inputs is odd.
• An XOR gate implements an exclusive OR, i.e., a true output result occurs if one – and
only one – of the gate’s inputs is true. If both inputs are false (i.e. LOW or 0) or both
inputs are true, the output is false.

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 EX-NOR
• The XNOR gate (also known as an XORN’T, ENOR, EXNOR or NXOR) – and
pronounced as Exclusive NOR – is a digital logic gate whose function is the logical
complement of the exclusive OR gate (XOR gate). Logically, an XNOR gate is a NOT
gate followed by an XOR gate.
• The XOR operation of inputs A and B is A ⊕ B; therefore, the XNOR operation of those
inputs will be (A + B) ̅. That means the output of the XOR gate is inverted in the XNOR
gate.

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 Example
Example 1
Q = A AND (B AND C)
Step 1 – Start with the brackets, this is the “B AND C” part.

Step 2 – Add the outer expression, this is the “A AND” part.

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 Example
Example 2.
Q = NOT (A OR B)
Step 1 – Start with the brackets, this is the “A OR B” part

Step 2 – Add the outer expression, this is the “NOT” part.

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